Background

This analysis document compliments FIA NLS Models: Biomass vs. Stand Age, G-Reconciled. All of the background information from that document applies to these analyses, which are extensions to them. The difference between that document and this analysis is the use of different data subsets.

Here, we fit the models using: 1) a temporally-balanced dataset, where we take the first and most-recent plot record for all plots in the dataset, 2) a temporally-balanced dataset (same as #1), but which excludes plot locations which have experienced harvest (at any point over the study interval 2000-2022)

Below the model fitting procedure is implemented by ecoprovince:

Analysis 1: Temporally-balanced analysis

211 - Northeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   4834     1203.6                                
## 2   4798     1069.7 36 133.94  16.688 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 52557.62
## 2     2 51701.49
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.45296    0.16808   2.695  0.00707 ** 
## alpha   0.85982    0.03444  24.965  < 2e-16 ***
## A     441.85673   32.45109  13.616  < 2e-16 ***
## k     185.76466   15.60336  11.905  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4722 on 4798 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 6.831e-06
##   (36 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in Mod.Sel3 %in% c(1, "1a", "1b", "1c", 4) : 
##   object 'Mod.Sel3' not found
## Error in Mod.Sel3 %in% c(1, "1a", "1b", "1c", 4) : 
##   object 'Mod.Sel3' not found
## Error in Mod.Sel3 %in% c(1, "1a", "1b", "1c", 4) : 
##   object 'Mod.Sel3' not found
##   model      AIC
## 1     2 51701.49
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.45296    0.16808   2.695  0.00707 ** 
## alpha   0.85982    0.03444  24.965  < 2e-16 ***
## A     441.85673   32.45109  13.616  < 2e-16 ***
## k     185.76466   15.60336  11.905  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4722 on 4798 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 6.831e-06
##   (36 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   4832     1179.6                                
## 2   4796     1035.9 36  143.7  18.481 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 51701.49
## 2     4 52463.90
## 3     5 51551.15
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.65379    0.18036   3.625 0.000292 ***
## alpha   0.85353    0.03265  26.139  < 2e-16 ***
## a      40.11843    1.93712  20.710  < 2e-16 ***
## b     108.90495    5.15248  21.136  < 2e-16 ***
## c     111.29913    4.38564  25.378  < 2e-16 ***
## d       0.89265    0.04335  20.590  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4647 on 4796 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (36 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.98547, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -29.391, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.

plotting 2

212 - Laurentian Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq   Df Sum Sq F value    Pr(>F)    
## 1  12943     5165.4                                  
## 2   9753     3585.0 3190 1580.4  1.3478 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 135621.4
## 2     2 102123.0
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.29724    0.14081   2.111   0.0348 *  
## alpha   0.70267    0.03058  22.981   <2e-16 ***
## A     176.59075    6.88136  25.662   <2e-16 ***
## k      65.09491    2.73847  23.771   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6063 on 9753 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 1.083e-06
##   (3205 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   9753     3585.0                                
## 2   9752     3519.8  1 65.171  180.56 < 2.2e-16 ***
## 3   9751     3435.0  1 84.865  240.91 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 102123.0
## 2    2a 101946.0
## 3    2b       NA
## 4    2c 101709.9
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau   4.146e-01  1.447e-01   2.866  0.00417 ** 
## alpha 7.877e-01  2.022e-02  38.958  < 2e-16 ***
## A     1.192e+02  5.082e+00  23.445  < 2e-16 ***
## k     4.626e+01  1.588e+00  29.129  < 2e-16 ***
## p     1.983e-01  9.842e-03  20.151  < 2e-16 ***
## s     2.363e+00  1.349e-01  17.510  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5935 on 9751 degrees of freedom
## 
## Number of iterations to convergence: 17 
## Achieved convergence tolerance: 6.728e-06
##   (3205 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: fits

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq   Df Sum Sq F value    Pr(>F)    
## 1  12941     5088.9                                  
## 2   9751     3422.9 3190   1666  1.4878 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2c 101709.9
## 2     4 135432.3
## 3     5 101675.5
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.43833    0.14548   3.013  0.00259 ** 
## alpha   0.79235    0.01979  40.034  < 2e-16 ***
## a      24.18608    0.95524  25.319  < 2e-16 ***
## b      82.87045    3.17194  26.126  < 2e-16 ***
## c     118.37742    5.24621  22.564  < 2e-16 ***
## d       1.24425    0.04485  27.744  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5925 on 9751 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (3205 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits

plot residuals

predict and plot

plotting 2

221 - Eastern Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   5442     948.80                                
## 2   5405     844.43 37 104.37  18.056 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 59550.63
## 2     2 58624.29
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.18125    0.12626   1.436    0.151    
## alpha   0.81310    0.03087  26.342   <2e-16 ***
## A     475.26137   28.14567  16.886   <2e-16 ***
## k     144.59688   10.07385  14.354   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3953 on 5405 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 8.453e-06
##   (37 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1   5405     844.43                          
## 2   5404     844.31  1 0.11852  0.7586 0.3838
##   model      AIC
## 1     2 58624.29
## 2    2a 58625.53
## 3    2b 58611.28
## 4    2c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.22671    0.12920   1.755   0.0794 .  
## alpha   0.81954    0.03110  26.352  < 2e-16 ***
## A     317.53226   27.47471  11.557  < 2e-16 ***
## k      72.74922    9.29982   7.823 6.18e-15 ***
## s       1.22840    0.06082  20.198  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3947 on 5404 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 2.529e-06
##   (37 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   5440     940.37                                
## 2   5403     834.50 37 105.87  18.526 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2b 58611.28
## 2     4 59506.03
## 3     5 58564.32
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.23356    0.12884   1.813   0.0699 .  
## alpha   0.81405    0.02994  27.189   <2e-16 ***
## a      29.92583    2.74687  10.895   <2e-16 ***
## b     166.53295    9.14543  18.209   <2e-16 ***
## c     142.75974   12.21268  11.689   <2e-16 ***
## d       1.37522    0.08076  17.028   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.393 on 5403 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (37 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits

plot residuals

predict and plot

## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.

plotting 2

222 - Midwest Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq  Df Sum Sq F value    Pr(>F)    
## 1   3547    1178.60                                 
## 2   2737     841.95 810 336.65  1.3511 2.251e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 38157.03
## 2     2 29481.92
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau    -0.05380    0.22291  -0.241    0.809    
## alpha   0.82138    0.05547  14.807  < 2e-16 ***
## A     490.38839   58.25668   8.418  < 2e-16 ***
## k     204.96549   26.97852   7.597 4.12e-14 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5546 on 2737 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 7.026e-06
##   (811 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1   2737     841.95                          
## 2   2736     841.65  1 0.29896  0.9718 0.3243
##   model      AIC
## 1     2 29481.92
## 2    2a 29482.95
## 3    2b       NA
## 4    2c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau    -0.05380    0.22291  -0.241    0.809    
## alpha   0.82138    0.05547  14.807  < 2e-16 ***
## A     490.38839   58.25668   8.418  < 2e-16 ***
## k     204.96549   26.97852   7.597 4.12e-14 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5546 on 2737 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 7.026e-06
##   (811 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq  Df Sum Sq F value    Pr(>F)    
## 1   3545    1160.08                                 
## 2   2735     816.94 810 343.14  1.4183 9.125e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 29481.92
## 2     4 38104.80
## 3     5 29403.25
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.10510    0.23599   0.445    0.656    
## alpha   0.84430    0.04755  17.755   <2e-16 ***
## a      26.79295    2.19579  12.202   <2e-16 ***
## b     119.86978    7.84054  15.288   <2e-16 ***
## c     104.72053    6.16485  16.987   <2e-16 ***
## d       1.01830    0.06210  16.399   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5465 on 2735 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (811 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.95843, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -17.144, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

223 - Central Interior Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq   Df Sum Sq F value    Pr(>F)    
## 1   6383     1208.6                                  
## 2   5254      961.6 1129 247.02  1.1954 4.219e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 66739.63
## 2     2 54968.25
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau    -0.24143    0.10087  -2.394   0.0167 *  
## alpha   0.75149    0.03396  22.126   <2e-16 ***
## A     280.04402   12.75403  21.957   <2e-16 ***
## k      75.92965    4.71986  16.087   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4278 on 5254 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 2.163e-06
##   (1130 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df   Sum Sq F value Pr(>F)
## 1   5254     961.60                           
## 2   5253     961.55  1 0.050724  0.2771 0.5986
##   model      AIC
## 1     2 54968.25
## 2    2a 54969.97
## 3    2b 54944.08
## 4    2c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau    -0.21532    0.10199  -2.111   0.0348 *  
## alpha   0.76003    0.03415  22.252   <2e-16 ***
## A     197.02836   11.07963  17.783   <2e-16 ***
## k      40.20400    3.15940  12.725   <2e-16 ***
## s       1.39168    0.07829  17.776   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4268 on 5253 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 4.49e-06
##   (1130 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq   Df Sum Sq F value    Pr(>F)    
## 1   6381    1195.86                                  
## 2   5252     944.25 1129 251.61  1.2396 1.039e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2b 54944.08
## 2     4 66675.81
## 3     5 54876.47
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau    -0.19990    0.10190  -1.962   0.0499 *  
## alpha   0.76139    0.03295  23.109   <2e-16 ***
## a      31.44052    2.90774  10.813   <2e-16 ***
## b     117.40892    5.13663  22.857   <2e-16 ***
## c     106.43481    6.07269  17.527   <2e-16 ***
## d       1.26371    0.07423  17.025   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.424 on 5252 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (1130 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits

plot residuals

predict and plot

plotting 2

231 - Southeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq  Df Sum Sq F value    Pr(>F)    
## 1   7773     2698.5                                 
## 2   7641     2403.0 132 295.47  7.1178 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 85845.56
## 2     2 84004.19
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     1.24455    0.16444   7.568 4.22e-14 ***
## alpha   0.61526    0.02415  25.474  < 2e-16 ***
## A     225.38333    8.98763  25.077  < 2e-16 ***
## k      51.58983    2.13778  24.132  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5608 on 7641 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 2.792e-06
##   (145 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("f_", Mod.Sel1, "b", sep = "")), data = G_231,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   7641     2403.0                                
## 2   7640     2305.6  1 97.387  322.71 < 2.2e-16 ***
## 3   7639     2248.7  1 56.920  193.36 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 84004.19
## 2    2a 83689.90
## 3    2b       NA
## 4    2c 83500.79
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     1.94524    0.20024   9.714   <2e-16 ***
## alpha   0.78032    0.01528  51.081   <2e-16 ***
## A     133.15240    5.75310  23.144   <2e-16 ***
## k      32.45965    1.18392  27.417   <2e-16 ***
## p       0.18680    0.00947  19.725   <2e-16 ***
## s       2.28738    0.12712  17.993   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5426 on 7639 degrees of freedom
## 
## Number of iterations to convergence: 15 
## Achieved convergence tolerance: 7.759e-06
##   (145 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: fits

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq  Df Sum Sq F value    Pr(>F)    
## 1   7771     2669.8                                 
## 2   7639     2247.0 132 422.83   10.89 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2c 83500.79
## 2     4 85766.57
## 3     5 83495.02
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     1.90303    0.19764   9.629   <2e-16 ***
## alpha   0.78032    0.01523  51.226   <2e-16 ***
## a      25.28966    0.92631  27.302   <2e-16 ***
## b     102.66192    4.92792  20.833   <2e-16 ***
## c     105.45753    7.79762  13.524   <2e-16 ***
## d       1.43411    0.06273  22.863   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5424 on 7639 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (145 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits

plot residuals

predict and plot

plotting 2

232 - Outer Coastal Plain Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq  Df Sum Sq F value    Pr(>F)    
## 1   7905     4072.2                                 
## 2   7735     3735.2 170    337  4.1052 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 88878.43
## 2     2 86870.95
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.87141    0.18185   4.792 1.68e-06 ***
## alpha   0.61236    0.02685  22.805  < 2e-16 ***
## A     226.00187   10.95493  20.630  < 2e-16 ***
## k      52.18677    2.65052  19.689  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6949 on 7735 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 9.209e-06
##   (201 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("f_", Mod.Sel1, "b", sep = "")), data = G_232,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1   7735     3735.2                                 
## 2   7734     3566.1  1 169.117  366.77 < 2.2e-16 ***
## 3   7733     3492.2  1  73.924  163.70 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 86870.95
## 2    2a 86514.38
## 3    2b       NA
## 4    2c 86354.27
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     1.42439    0.20918   6.809 1.05e-11 ***
## alpha   0.81600    0.01492  54.697  < 2e-16 ***
## A     138.37803    6.92119  19.993  < 2e-16 ***
## k      34.69364    1.48237  23.404  < 2e-16 ***
## p       0.20268    0.01124  18.025  < 2e-16 ***
## s       2.36450    0.15700  15.061  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.672 on 7733 degrees of freedom
## 
## Number of iterations to convergence: 28 
## Achieved convergence tolerance: 7.627e-06
##   (201 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: fits

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq  Df Sum Sq F value    Pr(>F)    
## 1   7903     4029.5                                 
## 2   7733     3489.9 170 539.64  7.0338 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2c 86354.27
## 2     4 88799.14
## 3     5 86349.26
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     1.38952    0.20683   6.718 1.97e-11 ***
## alpha   0.81558    0.01491  54.719  < 2e-16 ***
## a      28.36270    1.17948  24.047  < 2e-16 ***
## b     107.28397    6.15566  17.429  < 2e-16 ***
## c     114.33118   10.35916  11.037  < 2e-16 ***
## d       1.42115    0.07470  19.026  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6718 on 7733 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (201 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits

plot residuals

predict and plot

plotting 2

234 - Lower Mississippi Riverine Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    826     218.04                                
## 2    797     177.06 29 40.981  6.3612 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 9094.121
## 2     2 8721.045
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.38005    0.41044   0.926 0.354753    
## alpha   0.79101    0.06552  12.072  < 2e-16 ***
## A     727.26287  186.87440   3.892 0.000108 ***
## k     253.92949   73.93286   3.435 0.000624 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4713 on 797 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 7.387e-06
##   (29 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df   Sum Sq F value Pr(>F)
## 1    797     177.06                           
## 2    796     176.99  1 0.066994  0.3013 0.5832
##   model      AIC
## 1     2 8721.045
## 2    2a 8722.742
## 3    2b 8722.583
## 4    2c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.38005    0.41044   0.926 0.354753    
## alpha   0.79101    0.06552  12.072  < 2e-16 ***
## A     727.26287  186.87440   3.892 0.000108 ***
## k     253.92949   73.93286   3.435 0.000624 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4713 on 797 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 7.387e-06
##   (29 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    824     216.69                                
## 2    795     176.77 29 39.917  6.1905 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 8721.045
## 2     4 9092.966
## 3     5 8723.743
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.38005    0.41044   0.926 0.354753    
## alpha   0.79101    0.06552  12.072  < 2e-16 ***
## A     727.26287  186.87440   3.892 0.000108 ***
## k     253.92949   73.93286   3.435 0.000624 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4713 on 797 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 7.387e-06
##   (29 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.95645, p-value = 1.14e-14
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -9.7724, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

242 - Pacific Lowland Mixed Forest

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

251 - Prairie Parkland (Temperate)

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq  Df Sum Sq F value    Pr(>F)    
## 1   1387     347.56                                 
## 2    977     201.46 410  146.1  1.7282 5.294e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 14526.30
## 2     2 10147.91
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.55006    0.39958   1.377    0.169    
## alpha   0.73603    0.08646   8.513  < 2e-16 ***
## A     237.88617   31.29383   7.602 6.84e-14 ***
## k      97.25401   14.53331   6.692 3.71e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4541 on 977 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 4.859e-06
##   (411 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)   
## 1    977     201.46                              
## 2    976     199.66  1 1.7989  8.7938 0.003096 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 10147.91
## 2    2a 10141.11
## 3    2b 10131.28
## 4    2c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.53042    0.39173   1.354    0.176    
## alpha   0.75343    0.08629   8.731  < 2e-16 ***
## A     133.20058   14.88028   8.951  < 2e-16 ***
## k      36.74746    3.31677  11.079  < 2e-16 ***
## s       1.91517    0.23582   8.121 1.38e-15 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.45 on 976 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 9.775e-06
##   (411 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq  Df Sum Sq F value    Pr(>F)    
## 1   1385     337.23                                 
## 2    975     196.75 410 140.48  1.6979 2.506e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2b 10131.28
## 2     4 14488.37
## 3     5 10128.73
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.52834    0.39012   1.354  0.17595    
## alpha   0.75256    0.08617   8.734  < 2e-16 ***
## a      20.68236    7.88059   2.624  0.00881 ** 
## b      94.56738   11.99423   7.884 8.43e-15 ***
## c     104.72317   10.86129   9.642  < 2e-16 ***
## d       1.19567    0.16607   7.200 1.20e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4492 on 975 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (411 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.97093, p-value = 4.2e-13
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -7.8881, p-value = 3.068e-15
## alternative hypothesis: two.sided

predict and plot

plotting 2

255 - Prairie Parkland (Subtropical)

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)    
## 1    439     237.09                               
## 2    415     203.74 24 33.357  2.8311 1.41e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 4609.958
## 2     2 4397.209
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -0.1056     0.5547  -0.190  0.84905    
## alpha   0.5121     0.1326   3.862  0.00013 ***
## A     168.6419    32.7168   5.155 3.94e-07 ***
## k      48.6765    11.1115   4.381 1.50e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7007 on 415 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 3.1e-06
##   (25 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("f_", Mod.Sel1, "b", sep = "")), data = G_255,  : 
##   number of iterations exceeded maximum of 50
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    415     203.74                                
## 2    414     195.16  1 8.5821  18.206 2.459e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 4397.209
## 2    2a 4381.176
## 3    2b       NA
## 4    2c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.15195    0.60637   0.251    0.802    
## alpha   0.64504    0.09663   6.675 7.94e-11 ***
## A     351.27751  253.84534   1.384    0.167    
## k     210.90305  205.28194   1.027    0.305    
## p       0.04288    0.02451   1.749    0.081 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6866 on 414 degrees of freedom
## 
## Number of iterations to convergence: 17 
## Achieved convergence tolerance: 9.28e-06
##   (25 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    437     226.64                                
## 2    413     182.67 24  43.97  4.1422 8.462e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2a 4381.176
## 2     4 4594.028
## 3     5 4355.477
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    0.12210    0.57592   0.212    0.832    
## alpha  0.72207    0.08129   8.883  < 2e-16 ***
## a     24.95845    3.47359   7.185 3.16e-12 ***
## b     67.55158    9.95661   6.785 4.05e-11 ***
## c     54.80784    4.96595  11.037  < 2e-16 ***
## d      0.85562    0.11721   7.300 1.49e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6651 on 413 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (25 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.94116, p-value = 7.913e-12
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -5.1247, p-value = 2.98e-07
## alternative hypothesis: two.sided

predict and plot

plotting 2

261 - California Coastal Chaparral Forest and Shrub

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit

  • add s model: does not fit

  • add s+p model: does not fit

  • unable to fit model (only 64 observations)

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

262 - California Dry Steppe

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit

  • add s model: does not fit

  • add s+p model: does not fit

  • unable to fit model (0 observations)

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

263 - California Coastal Steppe - Mixed Forest and Redwood Forest

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

313 - Colorado Plateau Semi-Desert

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

315 - Southwest Plateau and Plains Dry Steppe and Shrub

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

321 - Chihuahuan Semi-Desert

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

322 - American Semidesert and Desert

model selection 1

## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
##   model AIC
## 1     1  NA
## 2     2  NA
## Warning in min(AIC1_322$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in get(paste("nls_322.", Mod.Sel1, sep = "")) : 
##   object 'nls_322.' not found

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"
  • Cannot fit model
  • not enough data (only 3 observations)

331 - Great Plains/Palouse Dry Steppe

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"
  • Cannot fit model

332 - Great Plains Steppe

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1    149     87.775                         
## 2    135     78.204 14 9.5719  1.1803 0.2973
##   model      AIC
## 1     1 1640.707
## 2     2 1511.918
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     2.1120     3.1747   0.665 0.507015    
## alpha   1.0245     0.2893   3.541 0.000547 ***
## A     156.2869   107.8495   1.449 0.149623    
## k      98.9969    67.6450   1.463 0.145662    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7611 on 135 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 4.794e-06
##   (15 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("f_", Mod.Sel1, "a", sep = "")), data = G_332,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("f_", Mod.Sel1, "b", sep = "")), data = G_332,  : 
##   number of iterations exceeded maximum of 50
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model      AIC
## 1     2 1511.918
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     2.1120     3.1747   0.665 0.507015    
## alpha   1.0245     0.2893   3.541 0.000547 ***
## A     156.2869   107.8495   1.449 0.149623    
## k      98.9969    67.6450   1.463 0.145662    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7611 on 135 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 4.794e-06
##   (15 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1    147     83.369                         
## 2    133     72.689 14 10.681  1.3959 0.1634
##   model      AIC
## 1     2 1511.918
## 2     4 1636.879
## 3     5 1505.753
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     2.4537     3.4077   0.720 0.472762    
## alpha   1.0341     0.2776   3.726 0.000287 ***
## a      23.3168    14.0511   1.659 0.099387 .  
## b      50.1805    35.1768   1.427 0.156061    
## c     117.3875    96.4037   1.218 0.225507    
## d       1.0737     0.7345   1.462 0.146177    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7393 on 133 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (15 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.87838, p-value = 2.671e-09
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -3.8886, p-value = 0.0001008
## alternative hypothesis: two.sided

predict and plot

plotting 2

341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit

plot residuals

## [1] "cannot plot residuals"
  • model not fitted because only 62 observations

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

342 - Intermountain Semi-Desert

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

411 - Everglades

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

M211 - Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   5103     963.25                                
## 2   5088     823.59 15 139.66   57.52 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 54262.24
## 2     2 53363.88
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.61018    0.16014    3.81  0.00014 ***
## alpha   0.80897    0.02637   30.68  < 2e-16 ***
## A     426.11432   26.45628   16.11  < 2e-16 ***
## k     183.74661   12.18665   15.08  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4023 on 5088 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 2.251e-06
##   (16 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   5088     823.59                                
## 2   5087     818.90  1 4.6942   29.16 6.965e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 53363.88
## 2    2a 53336.78
## 3    2b 53318.03
## 4    2c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.50399    0.15320    3.29  0.00101 ** 
## alpha   0.81807    0.02655   30.81  < 2e-16 ***
## A     241.28488   15.98660   15.09  < 2e-16 ***
## k      67.75381    6.25656   10.83  < 2e-16 ***
## s       1.34274    0.05479   24.51  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4005 on 5087 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 5.361e-06
##   (16 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   5101     952.58                                
## 2   5086     812.95 15 139.64   58.24 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2b 53318.03
## 2     4 54209.36
## 3     5 53301.62
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.54177    0.15584   3.476 0.000512 ***
## alpha   0.82011    0.02606  31.468  < 2e-16 ***
## a      19.48450    2.77004   7.034 2.27e-12 ***
## b     148.35643    9.29773  15.956  < 2e-16 ***
## c     170.73931   17.15590   9.952  < 2e-16 ***
## d       1.50104    0.09603  15.631  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3998 on 5086 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (16 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits

plot residuals

predict and plot

plotting 2

M221 - Eastern Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   5180     879.40                                
## 2   5152     813.08 28 66.326   15.01 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 57351.18
## 2     2 56719.09
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.68286    0.13121   5.204 2.02e-07 ***
## alpha   0.83316    0.04158  20.037  < 2e-16 ***
## A     260.95757    9.61560  27.139  < 2e-16 ***
## k      58.45777    2.94821  19.828  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3973 on 5152 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 1.421e-06
##   (30 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##   Res.Df Res.Sum Sq Df Sum Sq  F value Pr(>F)    
## 1   5152     813.08                              
## 2   5151     813.08  1  0.001   0.0064 0.9364    
## 3   5151     808.98  0  0.000                    
## 4   5150     789.87  1 19.115 124.6319 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 56719.09
## 2    2a 56721.09
## 3    2b 56695.08
## 4    2c 56573.79
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.85782    0.13912   6.166 7.54e-10 ***
## alpha   0.83626    0.03790  22.064  < 2e-16 ***
## A     160.54030    5.31529  30.203  < 2e-16 ***
## k      38.73561    1.03371  37.472  < 2e-16 ***
## p       0.25893    0.01761  14.700  < 2e-16 ***
## s       3.00269    0.23160  12.965  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3916 on 5150 degrees of freedom
## 
## Number of iterations to convergence: 10 
## Achieved convergence tolerance: 5.888e-06
##   (30 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   5178     862.65                                
## 2   5150     789.00 28 73.645  17.168 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2c 56573.79
## 2     4 57255.49
## 3     5 56568.14
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.84622    0.13822   6.122 9.92e-10 ***
## alpha   0.83474    0.03806  21.933  < 2e-16 ***
## a      40.58261    2.60780  15.562  < 2e-16 ***
## b     114.46846    4.25585  26.897  < 2e-16 ***
## c     100.35558    3.56301  28.166  < 2e-16 ***
## d       1.16211    0.05532  21.009  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3914 on 5150 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (30 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits

plot residuals

predict and plot

plotting 2

M223 - Ozark Broadleaf Forest Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    596     80.866                                
## 2    594     71.782  2 9.0843  37.587 4.262e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 6115.535
## 2     2 6038.933
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau    -0.08126    0.26259  -0.309    0.757    
## alpha   0.90022    0.09742   9.240  < 2e-16 ***
## A     296.62823   41.14427   7.209 1.72e-12 ***
## k      94.57333   18.56239   5.095 4.69e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3476 on 594 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 6.315e-06
##   (4 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = G_M223,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df   Sum Sq F value Pr(>F)
## 1    594     71.782                           
## 2    593     71.691  1 0.091014  0.7528 0.3859
##   model      AIC
## 1     2 6038.933
## 2    2a 6040.174
## 3    2b 6040.650
## 4    2c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau    -0.08126    0.26259  -0.309    0.757    
## alpha   0.90022    0.09742   9.240  < 2e-16 ***
## A     296.62823   41.14427   7.209 1.72e-12 ***
## k      94.57333   18.56239   5.095 4.69e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3476 on 594 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 6.315e-06
##   (4 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    594     80.723                                
## 2    592     71.703  2 9.0193  37.233 5.875e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 6038.933
## 2     4 6118.473
## 3     5 6042.280
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau    -0.08126    0.26259  -0.309    0.757    
## alpha   0.90022    0.09742   9.240  < 2e-16 ***
## A     296.62823   41.14427   7.209 1.72e-12 ***
## k      94.57333   18.56239   5.095 4.69e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3476 on 594 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 6.315e-06
##   (4 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.96672, p-value = 2.129e-10
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -8.7629, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

M231 - Ouachita Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    676     152.77                                
## 2    669     137.62  7 15.149  10.521 1.394e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 7025.553
## 2     2 6913.733
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     0.6315     0.5100   1.238    0.216    
## alpha   0.8739     0.1113   7.855 1.60e-14 ***
## A     286.5998    53.3736   5.370 1.09e-07 ***
## k     130.2058    27.4446   4.744 2.56e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4536 on 669 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 1.757e-06
##   (7 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    669     137.62                          
## 2    668     137.27  1 0.35126  1.7094 0.1915
##   model      AIC
## 1     2 6913.733
## 2    2a 6914.013
## 3    2b 6914.673
## 4    2c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     0.6315     0.5100   1.238    0.216    
## alpha   0.8739     0.1113   7.855 1.60e-14 ***
## A     286.5998    53.3736   5.370 1.09e-07 ***
## k     130.2058    27.4446   4.744 2.56e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4536 on 669 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 1.757e-06
##   (7 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    674     152.71                                
## 2    667     136.87  7 15.836  11.024 3.181e-13 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 6913.733
## 2     4 7029.273
## 3     5 6914.058
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     0.6315     0.5100   1.238    0.216    
## alpha   0.8739     0.1113   7.855 1.60e-14 ***
## A     286.5998    53.3736   5.370 1.09e-07 ***
## k     130.2058    27.4446   4.744 2.56e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4536 on 669 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 1.757e-06
##   (7 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.96065, p-value = 1.886e-12
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -8.6968, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

M242 - Cascade Mixed Forest

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

M261 - Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq  Df Sum Sq F value Pr(>F)
## 1    326    100.337                          
## 2    159     52.836 167 47.502   0.856 0.8395
##   model      AIC
## 1     1 3504.259
## 2     2 1757.521
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)   
## tau    -1.4911     1.4021  -1.064  0.28917   
## alpha   0.7692     0.2686   2.864  0.00475 **
## A     199.4827   135.7096   1.470  0.14356   
## k      14.6863    10.3710   1.416  0.15870   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5765 on 159 degrees of freedom
## 
## Number of iterations to convergence: 12 
## Achieved convergence tolerance: 5.404e-06
##   (167 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    159     52.836                          
## 2    158     52.385  1 0.45081  1.3597 0.2453
##   model      AIC
## 1     2 1757.521
## 2    2a 1758.125
## 3    2b       NA
## 4    2c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)   
## tau    -1.4911     1.4021  -1.064  0.28917   
## alpha   0.7692     0.2686   2.864  0.00475 **
## A     199.4827   135.7096   1.470  0.14356   
## k      14.6863    10.3710   1.416  0.15870   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5765 on 159 degrees of freedom
## 
## Number of iterations to convergence: 12 
## Achieved convergence tolerance: 5.404e-06
##   (167 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq  Df Sum Sq F value Pr(>F)
## 1    324     96.856                          
## 2    157     50.310 167 46.546  0.8698 0.8127
##   model      AIC
## 1     2 1757.521
## 2     4 3496.641
## 3     5 1753.538
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -1.5154     1.3312  -1.138   0.2567    
## alpha   0.6590     0.2942   2.240   0.0265 *  
## a       0.0000   141.2170   0.000   1.0000    
## b     188.9583   180.2107   1.049   0.2960    
## c     113.2014    16.3494   6.924 1.06e-10 ***
## d       1.7043     0.9728   1.752   0.0817 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5661 on 157 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (167 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.98242, p-value = 0.03655
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = 0.2756, p-value = 0.7829
## alternative hypothesis: two.sided

predict and plot

plotting 2

M262 - California coastal range - coniferous forest - open woodland - shrub meadow

Model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit

plot residuals

## [1] "cannot plot residuals"
  • model can fit - but K is negative (only 19 observations) - model excluded

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M313 - Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M331 - Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M332 - Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M333 - Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M334 - Black Hills Coniferous Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1    299    124.348                         
## 2    213     86.589 86 37.759    1.08 0.3252
##   model      AIC
## 1     1 3013.807
## 2     2 2166.492
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -0.5945     0.8052  -0.738 0.461088    
## alpha   0.7886     0.1334   5.913 1.32e-08 ***
## A     117.3902    32.3159   3.633 0.000352 ***
## k      50.8451    22.4857   2.261 0.024756 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6376 on 213 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 9.886e-06
##   (89 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##   Res.Df Res.Sum Sq Df   Sum Sq F value Pr(>F)
## 1    213     86.589                           
## 2    212     86.587  1 0.002415  0.0059 0.9388
## 3    212     86.462  0 0.000000               
## 4    211     86.173  1 0.288651  0.7068 0.4015
##   model      AIC
## 1     2 2166.492
## 2    2a 2168.486
## 3    2b 2168.172
## 4    2c 2169.446
## Warning in `[<-.data.frame`(`*tmp*`, nls.param.df_bal$Code == "M334", , :
## provided 33 variables to replace 32 variables
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -0.5945     0.8052  -0.738 0.461088    
## alpha   0.7886     0.1334   5.913 1.32e-08 ***
## A     117.3902    32.3159   3.633 0.000352 ***
## k      50.8451    22.4857   2.261 0.024756 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6376 on 213 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 9.886e-06
##   (89 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1    297    124.069                         
## 2    211     86.545 86 37.523  1.0638 0.3565
##   model      AIC
## 1     2 2166.492
## 2     4 3017.126
## 3     5 2170.381
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -0.5945     0.8052  -0.738 0.461088    
## alpha   0.7886     0.1334   5.913 1.32e-08 ***
## A     117.3902    32.3159   3.633 0.000352 ***
## k      50.8451    22.4857   2.261 0.024756 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6376 on 213 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 9.886e-06
##   (89 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.92294, p-value = 3.195e-09
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -2.5717, p-value = 0.01012
## alternative hypothesis: two.sided

predict and plot

plotting 2

M341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2


Fitted parameters

Best / selected models by ecoprovince

Code Ecoregion Sel.Mod.2 Sel.Mod.3 Best.Mod
211 Northeastern Mixed Forest 2 5 5
212 Laurentian Mixed Forest 2c 5 5
221 Eastern Broadleaf Forest 2b 5 5
222 Midwest Broadleaf Forest 2 5 5
223 Central Interior Broadleaf Forest 2b 5 5
231 Southeastern Mixed Forest 2c 5 5
232 Outer Coastal Plain Mixed Forest 2c 5 5
234 Lower Mississippi Riverine Forest 2 2 2
242 Pacific Lowland Mixed Forest NA NA NA
251 Prairie Parkland (Temperate) 2b 5 5
255 Prairie Parkland (Subtropical) 2a 5 5
261 California Coastal Chaparral Forest and Shrub NA NA NA
262 California Dry Steppe NA NA NA
263 California Coastal Steppe - Mixed Forest and Redwood Forest NA NA NA
313 Colorado Plateau Semi-Desert NA NA NA
315 Southwest Plateau and Plains Dry Steppe and Shrub NA NA NA
321 Chihuahuan Semi-Desert NA NA NA
322 American Semidesert and Desert NA NA NA
331 Great Plains/Palouse Dry Steppe NA NA NA
332 Great Plains Steppe 2 5 5
341 Intermountain Semi-Desert and Desert NA NA NA
342 Intermountain Semi-Desert NA NA NA
411 Everglades NA NA NA
M211 Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow 2b 5 5
M221 Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow 2c 5 5
M223 Ozark Broadleaf Forest Meadow 2 2 2
M231 Ouachita Mixed Forest 2 2 2
M242 Cascade Mixed Forest NA NA NA
M261 Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow 2 5 5
M262 California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow NA NA NA
M313 Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow NA NA NA
M331 Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow NA NA NA
M332 Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow NA NA NA
M333 Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow NA NA NA
M334 Black Hills Coniferous Forest 2 2 2
M341 Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow NA NA NA

table by ecoprovince

Code Ecoregion region n.obs n.plots tau tau.variance tau.2.5 tau.97.5 alpha alpha.variance alpha.2.5 alpha.97.5 A A.2.5 A.97.5 k k.2.5 k.97.5 a a.2.5 a.97.5 b b.se b.2.5 b.97.5 c c.2.5 c.97.5 d d.2.5 d.97.5
211 Northeastern Mixed Forest east 4838 2419 0.6537893 0.0325313 0.3001925 1.0073861 0.8535320 0.0010662 0.7895172 0.9175468 441.8567 378.23771 505.4757 185.76466 155.174910 216.35440 40.11843 36.320789 43.91608 108.90495 NA 98.80371 119.00618 111.29913 102.70126 119.89700 0.8926520 0.8076609 0.9776431
212 Laurentian Mixed Forest east 12962 6481 0.4383266 0.0211649 0.1531525 0.7235006 0.7923513 0.0003917 0.7535546 0.8311479 119.1542 109.19192 129.1164 46.26337 43.150146 49.37658 24.18608 22.313610 26.05854 82.87045 NA 76.65278 89.08812 118.37742 108.09375 128.66108 1.2442510 1.1563415 1.3321605
221 Eastern Broadleaf Forest east 5446 2723 0.2335591 0.0166007 -0.0190263 0.4861445 0.8140497 0.0008964 0.7553542 0.8727451 317.5323 263.67075 371.3938 72.74922 54.517828 90.98061 29.92583 24.540863 35.31080 166.53295 NA 148.60422 184.46167 142.75974 118.81797 166.70151 1.3752196 1.2168890 1.5335502
222 Midwest Broadleaf Forest east 3552 1776 0.1050960 0.0556931 -0.3576483 0.5678403 0.8442958 0.0022613 0.7510516 0.9375400 490.3884 376.15688 604.6199 204.96549 152.065171 257.86581 26.79295 22.487375 31.09852 119.86978 NA 104.49581 135.24375 104.72053 92.63230 116.80876 1.0183031 0.8965441 1.1400621
223 Central Interior Broadleaf Forest east 6388 3194 -0.1998960 0.0103846 -0.3996715 -0.0001205 0.7613860 0.0010855 0.6967954 0.8259766 197.0284 175.30767 218.7490 40.20400 34.010267 46.39773 31.44052 25.740151 37.14089 117.40892 NA 107.33898 127.47885 106.43481 94.52981 118.33982 1.2637077 1.1181891 1.4092263
231 Southeastern Mixed Forest east 7790 3895 1.9030292 0.0390616 1.5156002 2.2904583 0.7803161 0.0002320 0.7504558 0.8101765 133.1524 121.87475 144.4300 32.45965 30.138849 34.78046 25.28966 23.473843 27.10548 102.66192 NA 93.00185 112.32199 105.45753 90.17205 120.74300 1.4341111 1.3111510 1.5570712
232 Outer Coastal Plain Mixed Forest east 7940 3970 1.3895246 0.0427791 0.9840796 1.7949695 0.8155816 0.0002222 0.7863637 0.8447994 138.3780 124.81063 151.9454 34.69364 31.787789 37.59950 28.36270 26.050590 30.67481 107.28397 NA 95.21721 119.35073 114.33118 94.02442 134.63794 1.4211487 1.2747245 1.5675729
234 Lower Mississippi Riverine Forest east 830 415 0.3800485 0.1684627 -0.4256268 1.1857237 0.7910134 0.0042932 0.6623967 0.9196302 727.2629 360.43872 1094.0870 253.92949 108.803351 399.05563 NA NA NA NA NA NA NA NA NA NA NA NA NA
242 Pacific Lowland Mixed Forest pacific 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
251 Prairie Parkland (Temperate) east 1392 696 0.5283410 0.1521922 -0.2372270 1.2939089 0.7525582 0.0074250 0.5834615 0.9216549 133.2006 103.99955 162.4016 36.74746 30.238646 43.25628 20.68236 5.217490 36.14724 94.56738 NA 71.02990 118.10487 104.72317 83.40898 126.03736 1.1956671 0.8697794 1.5215548
255 Prairie Parkland (Subtropical) east 444 222 0.1220981 0.3316784 -1.0099927 1.2541890 0.7220663 0.0066076 0.5622786 0.8818540 351.2775 -147.70896 850.2640 210.90305 -192.621828 614.42793 24.95845 18.130329 31.78658 67.55158 NA 47.97963 87.12353 54.80784 45.04615 64.56953 0.8556187 0.6252087 1.0860287
261 California Coastal Chaparral Forest and Shrub pacific 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
262 California Dry Steppe pacific 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
263 California Coastal Steppe - Mixed Forest and Redwood Forest pacific 4 2 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
313 Colorado Plateau Semi-Desert interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
315 Southwest Plateau and Plains Dry Steppe and Shrub interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
321 Chihuahuan Semi-Desert interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
322 American Semidesert and Desert interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
331 Great Plains/Palouse Dry Steppe interior west 118 59 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
332 Great Plains Steppe interior west 154 77 2.4536877 11.6123801 -4.2865995 9.1939750 1.0341031 0.0770453 0.4850798 1.5831264 156.2869 -57.00625 369.5801 98.99687 -34.784176 232.77792 23.31681 -4.475821 51.10943 50.18053 NA -19.39784 119.75890 117.38752 -73.29536 308.07039 1.0736506 -0.3791879 2.5264891
341 Intermountain Semi-Desert and Desert interior west 4 2 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
342 Intermountain Semi-Desert interior west 2 1 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
411 Everglades east 66 33 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M211 Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow east 5108 2554 0.5417730 0.0242861 0.2362595 0.8472865 0.8201066 0.0006792 0.7690154 0.8711978 241.2849 209.94426 272.6255 67.75381 55.488265 80.01935 19.48450 14.054022 24.91497 148.35643 NA 130.12888 166.58398 170.73931 137.10636 204.37226 1.5010388 1.3127853 1.6892923
M221 Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow east 5186 2593 0.8462159 0.0191060 0.5752376 1.1171943 0.8347375 0.0014485 0.7601251 0.9093499 160.5403 150.12007 170.9605 38.73561 36.709097 40.76212 40.58261 35.470220 45.69500 114.46846 NA 106.12519 122.81174 100.35558 93.37058 107.34059 1.1621055 1.0536627 1.2705482
M223 Ozark Broadleaf Forest Meadow east 602 301 -0.0812639 0.0689520 -0.5969759 0.4344482 0.9002204 0.0094914 0.7088835 1.0915572 296.6282 215.82228 377.4342 94.57333 58.117443 131.02922 NA NA NA NA NA NA NA NA NA NA NA NA NA
M231 Ouachita Mixed Forest east 680 340 0.6315443 0.2600526 -0.3697578 1.6328464 0.8739198 0.0123794 0.6554535 1.0923861 286.5998 181.79982 391.3997 130.20582 76.317969 184.09368 NA NA NA NA NA NA NA NA NA NA NA NA NA
M242 Cascade Mixed Forest pacific 34 17 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M261 Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow pacific 330 165 -1.5153914 1.7720212 -4.1447096 1.1139269 0.6589855 0.0865469 0.0779075 1.2400635 199.4827 -68.54334 467.5088 14.68629 -5.796325 35.16890 0.00000 -278.930355 278.93036 188.95825 NA -166.99203 544.90854 113.20139 80.90831 145.49447 1.7042560 -0.2172067 3.6257187
M262 California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow interior west 8 4 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M313 Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M331 Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M332 Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow interior west 20 10 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M333 Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow interior west 22 11 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M334 Black Hills Coniferous Forest interior west 306 153 -0.5945383 0.6483121 -2.1816767 0.9926002 0.7885811 0.0177862 0.5256970 1.0514651 117.3902 53.69020 181.0901 50.84512 6.522162 95.16807 NA NA NA NA NA NA NA NA NA NA NA NA NA
M341 Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA

plot tau

map

## OGR data source with driver: ESRI Shapefile 
## Source: "C:\Users\hogan.jaaron\Dropbox\FIA_R\Mapping\S_USA.EcoMapProvinces\S_USA.EcoMapProvinces.shp", layer: "S_USA.EcoMapProvinces"
## with 37 features
## It has 17 fields
## Integer64 fields read as strings:  PROVINCE_ PROVINCE_I

plot alpha (biomass compensation effect)

plot A (asymptote of B)

## Warning: Removed 19 rows containing missing values (`geom_point()`).

plot k (stand age at half biomass asymptote)

## Warning: Removed 19 rows containing missing values (`geom_point()`).

Caclulations - weighted averages

tau (productivity trend in % 2000-2021)

##          region weighted.tau weighted.tau.std_Error 95 % CI, upper
## 1     entire US  0.675858940            0.056786257    0.787160003
## 2       pacific -0.007786242            0.006839707    0.005619585
## 3          east  0.680594405            0.055645458    0.789659503
## 4 interior west  0.003050777            0.009026644    0.020743000
##   95 % CI, lower
## 1     0.56455788
## 2    -0.02119207
## 3     0.57152931
## 4    -0.01464145

alpha (biomass compensation effect)

##          region weighted.alpha weighted.alpha.std_Error 95 % CI, upper
## 1     entire US    0.802590633             0.0087480764    0.819736862
## 2       pacific    0.003385937             0.0015115719    0.006348618
## 3          east    0.792968005             0.0085672217    0.809759759
## 4 interior west    0.006236691             0.0009201648    0.008040214
##   95 % CI, lower
## 1   0.7854444031
## 2   0.0004232565
## 3   0.7761762504
## 4   0.0044331675

A (asymptote of forest biomass in Mg/ha)

##          region weighted.A
## 1     entire US   218.8716
## 2       pacific   178.8840
## 3          east   220.3503
## 4 interior west     0.0000

K (stand age at half maturation in years)

##          region weighted.k
## 1     entire US   69.93156
## 2       pacific   13.16977
## 3          east   70.47598
## 4 interior west   48.58695

Model Bookeeping

1. Delta-B due to Delta-STDAGE

2. Delta-B due to Delta-Year (ge)

make a fig

## Warning: Removed 12502 rows containing missing values (`geom_point()`).

3. stand age densities

make a fig

## Warning: package 'ggridges' was built under R version 4.2.2
## Picking joint bandwidth of 7.36
## Warning: Using the `size` aesthietic with geom_segment was deprecated in ggplot2 3.4.0.
## ℹ Please use the `linewidth` aesthetic instead.


Analysis 2: Temporally-balanced, No-harvest

211 - Northeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   3758     873.45                                
## 2   3726     802.88 32 70.566  10.234 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 40904.91
## 2     2 40336.15
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.76055    0.21445   3.546 0.000395 ***
## alpha   1.18877    0.06983  17.023  < 2e-16 ***
## A     424.79024   35.65526  11.914  < 2e-16 ***
## k     186.51949   17.45686  10.685  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4642 on 3726 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 6.291e-06
##   (32 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df     Sum Sq F value Pr(>F)
## 1   3726     802.88                             
## 2   3725     802.88  1 0.00036442  0.0017 0.9672
##   model      AIC
## 1     2 40336.15
## 2    2a 40338.14
## 3    2b 40332.46
## 4    2c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.72837    0.21189   3.437 0.000594 ***
## alpha   1.19404    0.07036  16.970  < 2e-16 ***
## A     296.71063   41.45441   7.158 9.85e-13 ***
## k      99.70219   21.80438   4.573 4.97e-06 ***
## s       1.17105    0.07830  14.955  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4639 on 3725 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 2.716e-06
##   (32 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   3756     857.29                                
## 2   3724     782.82 32  74.47  11.071 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2b 40332.46
## 2     4 40838.67
## 3     5 40245.74
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.94240    0.22839   4.126 3.77e-05 ***
## alpha   1.17324    0.06877  17.060  < 2e-16 ***
## a      37.60901    2.18639  17.201  < 2e-16 ***
## b     107.76147    6.14881  17.526  < 2e-16 ***
## c     115.49056    5.62271  20.540  < 2e-16 ***
## d       0.93145    0.05282  17.634  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4585 on 3724 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (32 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.98688, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -26.722, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

212 - Laurentian Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq   Df Sum Sq F value    Pr(>F)    
## 1  10460     3892.5                                  
## 2   7876     2754.4 2584 1138.1  1.2594 1.108e-13 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model       AIC
## 1     1 109465.57
## 2     2  82497.09
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.33597    0.15467   2.172   0.0299 *  
## alpha   0.91328    0.04644  19.664   <2e-16 ***
## A     174.20937    7.60537  22.906   <2e-16 ***
## k      66.00906    3.16091  20.883   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5914 on 7876 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 3.674e-06
##   (2590 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   7876     2754.4                                
## 2   7875     2750.2  1  4.214  12.067  0.000516 ***
## 3   7875     2754.4  0  0.000                      
## 4   7874     2718.8  1 35.554 102.968 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 82497.09
## 2    2a 82487.02
## 3    2b 82498.96
## 4    2c 82398.59
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.41760    0.15914   2.624   0.0087 ** 
## alpha   0.90560    0.04343  20.850   <2e-16 ***
## A     118.34768    5.85244  20.222   <2e-16 ***
## k      45.43189    1.92530  23.597   <2e-16 ***
## p       0.18195    0.01521  11.962   <2e-16 ***
## s       2.11897    0.15531  13.644   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5876 on 7874 degrees of freedom
## 
## Number of iterations to convergence: 12 
## Achieved convergence tolerance: 8.519e-06
##   (2590 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq   Df Sum Sq F value    Pr(>F)    
## 1  10458     3839.4                                  
## 2   7874     2711.2 2584 1128.2   1.268 2.114e-14 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model       AIC
## 1    2c  82398.59
## 2     4 109325.84
## 3     5  82376.63
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.44439    0.16044    2.77  0.00562 ** 
## alpha   0.90815    0.04322   21.01  < 2e-16 ***
## a      22.73882    1.25331   18.14  < 2e-16 ***
## b      81.87877    3.62787   22.57  < 2e-16 ***
## c     123.26490    6.80062   18.13  < 2e-16 ***
## d       1.33519    0.06078   21.97  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5868 on 7874 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (2590 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits

plot residuals

predict and plot

plotting 2

221 - Eastern Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   4456      722.5                                
## 2   4422      670.6 34 51.894  10.065 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 48766.23
## 2     2 48164.75
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     0.5204     0.1598   3.257  0.00113 ** 
## alpha   0.9229     0.0519  17.783  < 2e-16 ***
## A     444.0211    29.4187  15.093  < 2e-16 ***
## k     143.4409    10.9490  13.101  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3894 on 4422 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 3.693e-06
##   (34 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)   
## 1   4422     670.60                              
## 2   4421     669.51  1 1.0958  7.2361 0.007172 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 48164.75
## 2    2a 48159.51
## 3    2b 48142.92
## 4    2c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.57536    0.16350   3.519 0.000437 ***
## alpha   0.93260    0.05238  17.805  < 2e-16 ***
## A     269.98555   21.83371  12.366  < 2e-16 ***
## k      61.89490    6.76412   9.150  < 2e-16 ***
## s       1.33526    0.07232  18.463  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3884 on 4421 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 8.035e-06
##   (34 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   4454     713.75                                
## 2   4420     662.39 34 51.355  10.079 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2b 48142.92
## 2     4 48715.91
## 3     5 48114.23
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.60426    0.16462   3.671 0.000245 ***
## alpha   0.92476    0.05168  17.894  < 2e-16 ***
## a      27.90793    3.08437   9.048  < 2e-16 ***
## b     151.78065    8.69980  17.446  < 2e-16 ***
## c     133.03972   10.63119  12.514  < 2e-16 ***
## d       1.31816    0.08221  16.034  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3871 on 4420 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (34 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.98521, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -27.63, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

222 - Midwest Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq  Df Sum Sq F value  Pr(>F)    
## 1   2793     944.73                               
## 2   2141     671.57 652 273.16  1.3357 1.3e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 30090.45
## 2     2 23141.64
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.01599    0.26220   0.061    0.951    
## alpha   0.94372    0.07917  11.921  < 2e-16 ***
## A     532.48363   78.56953   6.777 1.58e-11 ***
## k     233.87556   37.87205   6.175 7.87e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5601 on 2141 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 2.209e-06
##   (653 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)   
## 1   2141     671.57                              
## 2   2140     669.22  1 2.3525  7.5226 0.006144 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 23141.64
## 2    2a 23136.12
## 3    2b       NA
## 4    2c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.04294    0.26500   0.162    0.871    
## alpha   0.96046    0.07927  12.116  < 2e-16 ***
## A     400.61334   62.34054   6.426 1.61e-10 ***
## k     146.96501   32.54757   4.515 6.66e-06 ***
## p      -0.02205    0.01203  -1.833    0.067 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5592 on 2140 degrees of freedom
## 
## Number of iterations to convergence: 10 
## Achieved convergence tolerance: 5.035e-06
##   (653 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq  Df Sum Sq F value    Pr(>F)    
## 1   2791     928.22                                 
## 2   2139     655.15 652 273.08  1.3675 1.788e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2a 23136.12
## 2     4 30045.16
## 3     5 23092.53
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.22531    0.28454   0.792    0.429    
## alpha   0.97643    0.07549  12.934   <2e-16 ***
## a      24.12342    2.50787   9.619   <2e-16 ***
## b     119.93339    9.21897  13.009   <2e-16 ***
## c     106.27003    7.30330  14.551   <2e-16 ***
## d       1.04004    0.07193  14.458   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5534 on 2139 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (653 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.96143, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -16.089, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

223 - Central Interior Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq  Df Sum Sq F value Pr(>F)
## 1   5108     929.31                          
## 2   4258     769.03 850 160.28  1.0441  0.204
##   model      AIC
## 1     1 53477.85
## 2     2 44746.37
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau    -0.13289    0.11833  -1.123    0.261    
## alpha   0.85046    0.05658  15.031   <2e-16 ***
## A     295.93377   15.87888  18.637   <2e-16 ***
## k      86.90263    6.09681  14.254   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.425 on 4258 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 1.55e-06
##   (850 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1   4258     769.03                          
## 2   4257     768.80  1 0.23249  1.2874 0.2566
##   model      AIC
## 1     2 44746.37
## 2    2a 44747.08
## 3    2b 44714.13
## 4    2c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau    -0.10426    0.11946  -0.873    0.383    
## alpha   0.86326    0.05695  15.157   <2e-16 ***
## A     191.83961   11.12995  17.236   <2e-16 ***
## k      40.42488    3.02139  13.380   <2e-16 ***
## s       1.48176    0.08512  17.408   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4233 on 4257 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 8.362e-06
##   (850 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq  Df Sum Sq F value  Pr(>F)  
## 1   5106     913.48                             
## 2   4256     751.00 850 162.49  1.0833 0.06283 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2b 44714.13
## 2     4 53394.02
## 3     5 44649.23
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau    -0.08864    0.11921  -0.744    0.457    
## alpha   0.85186    0.05587  15.248   <2e-16 ***
## a      29.94864    2.86870  10.440   <2e-16 ***
## b     116.92622    5.31187  22.012   <2e-16 ***
## c     104.05803    5.72271  18.183   <2e-16 ***
## d       1.20947    0.07174  16.859   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4201 on 4256 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (850 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits

plot residuals

predict and plot

plotting 2

231 - Southeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq  Df Sum Sq F value    Pr(>F)    
## 1   6088     1450.4                                 
## 2   5969     1320.6 119 129.79  4.9297 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 66409.03
## 2     2 64981.78
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     1.49368    0.17211   8.678   <2e-16 ***
## alpha   0.82503    0.04795  17.207   <2e-16 ***
## A     249.29183   10.49290  23.758   <2e-16 ***
## k      65.06575    2.81839  23.086   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4704 on 5969 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 7.397e-06
##   (119 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1   5969     1320.6                                 
## 2   5968     1319.8  1  0.7796   3.525    0.0605 .  
## 3   5968     1320.2  0  0.0000                      
## 4   5967     1308.2  1 11.9851  54.665 1.626e-13 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 64981.78
## 2    2a 64980.25
## 3    2b 64981.97
## 4    2c 64929.50
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     1.58501    0.17775   8.917  < 2e-16 ***
## alpha   0.83513    0.04688  17.813  < 2e-16 ***
## A     160.41210    8.46170  18.957  < 2e-16 ***
## k      34.73716    1.94017  17.904  < 2e-16 ***
## p       0.09852    0.01425   6.912 5.27e-12 ***
## s       1.69148    0.11557  14.636  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4682 on 5967 degrees of freedom
## 
## Number of iterations to convergence: 12 
## Achieved convergence tolerance: 9.731e-06
##   (119 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq  Df Sum Sq F value    Pr(>F)    
## 1   6086     1437.5                                 
## 2   5967     1307.1 119 130.34  5.0002 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2c 64929.50
## 2     4 66358.45
## 3     5 64924.45
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     1.56840    0.17681   8.871   <2e-16 ***
## alpha   0.83422    0.04685  17.805   <2e-16 ***
## a      16.88730    1.63137  10.352   <2e-16 ***
## b     127.95506    7.55556  16.935   <2e-16 ***
## c     137.97804   16.47016   8.377   <2e-16 ***
## d       1.78789    0.10347  17.279   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.468 on 5967 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (119 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits

plot residuals

predict and plot

plotting 2

232 - Outer Coastal Plain Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq  Df Sum Sq F value    Pr(>F)    
## 1   6290     2432.4                                 
## 2   6150     2239.5 140 192.94  3.7845 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 70632.57
## 2     2 69030.05
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     1.05946    0.19441    5.45 5.24e-08 ***
## alpha   0.78664    0.04693   16.76  < 2e-16 ***
## A     258.22071   13.82230   18.68  < 2e-16 ***
## k      69.01364    3.82624   18.04  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6034 on 6150 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 4.681e-06
##   (142 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1   6150     2239.5                                 
## 2   6149     2233.3  1  6.1935  17.052 3.684e-05 ***
## 3   6149     2239.3  0  0.0000                      
## 4   6148     2213.4  1 25.8828  71.891 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 69030.05
## 2    2a 69015.01
## 3    2b 69031.60
## 4    2c 68962.05
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     1.19119    0.20278   5.874 4.47e-09 ***
## alpha   0.81085    0.04401  18.425  < 2e-16 ***
## A     158.53548    9.39510  16.874  < 2e-16 ***
## k      36.29188    2.12763  17.057  < 2e-16 ***
## p       0.12742    0.01578   8.075 8.06e-16 ***
## s       1.87087    0.14548  12.860  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6 on 6148 degrees of freedom
## 
## Number of iterations to convergence: 17 
## Achieved convergence tolerance: 5.625e-06
##   (142 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq  Df Sum Sq F value    Pr(>F)    
## 1   6288     2414.5                                 
## 2   6148     2212.5 140 202.02  4.0099 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2c 68962.05
## 2     4 70589.95
## 3     5 68959.28
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     1.17160    0.20149   5.815 6.38e-09 ***
## alpha   0.80939    0.04399  18.399  < 2e-16 ***
## a      20.89438    1.77891  11.746  < 2e-16 ***
## b     127.00119    8.66265  14.661  < 2e-16 ***
## c     137.92562   17.86323   7.721 1.34e-14 ***
## d       1.67730    0.11014  15.229  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5999 on 6148 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (142 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits

plot residuals

predict and plot

plotting 2

234 - Lower Mississippi Riverine Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    675     158.75                                
## 2    653     137.82 22 20.932  4.5079 7.916e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 7483.277
## 2     2 7228.714
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     0.5365     0.4799   1.118 0.264026    
## alpha   0.8974     0.1033   8.688  < 2e-16 ***
## A     578.9666   141.8010   4.083    5e-05 ***
## k     194.2614    54.2443   3.581 0.000367 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4594 on 653 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 1.838e-06
##   (27 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = G_234,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df   Sum Sq F value Pr(>F)
## 1    653     137.82                           
## 2    652     137.77  1 0.053795  0.2546  0.614
##   model      AIC
## 1     2 7228.714
## 2    2a 7230.457
## 3    2b 7230.618
## 4    2c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     0.5365     0.4799   1.118 0.264026    
## alpha   0.8974     0.1033   8.688  < 2e-16 ***
## A     578.9666   141.8010   4.083    5e-05 ***
## k     194.2614    54.2443   3.581 0.000367 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4594 on 653 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 1.838e-06
##   (27 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

model selection 3

## Error in nls(f_5, data = G_234, start = c(tau = tau.start, alpha = alpha.start,  : 
##   Convergence failure: iteration limit reached without convergence (10)
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq   Df  Sum Sq F value Pr(>F)
## 1    673     158.11                            
## 2    795     176.77 -122 -18.654  0.6508 0.9981
##   model      AIC
## 1     2 7228.714
## 2     4 7484.532
## 3     5 8723.743
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     0.5365     0.4799   1.118 0.264026    
## alpha   0.8974     0.1033   8.688  < 2e-16 ***
## A     578.9666   141.8010   4.083    5e-05 ***
## k     194.2614    54.2443   3.581 0.000367 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4594 on 653 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 1.838e-06
##   (27 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.96055, p-value = 2.77e-12
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -9.2684, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

242 - Pacific Lowland Mixed Forest

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

251 - Prairie Parkland (Temperate)

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq  Df Sum Sq F value    Pr(>F)    
## 1   1213     319.61                                 
## 2    866     178.11 347 141.49  1.9826 9.693e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model       AIC
## 1     1 12758.145
## 2     2  9001.833
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     0.5936     0.4321   1.374     0.17    
## alpha   0.7574     0.1119   6.767 2.42e-11 ***
## A     240.5767    34.4469   6.984 5.72e-12 ***
## k      99.7638    16.3415   6.105 1.55e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4535 on 866 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 2.039e-06
##   (348 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    866     178.11                          
## 2    865     177.69  1 0.42531  2.0705 0.1505
##   model      AIC
## 1     2 9001.833
## 2    2a 9001.753
## 3    2b 8998.361
## 4    2c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     0.5812     0.4286   1.356    0.175    
## alpha   0.7736     0.1123   6.891 1.07e-11 ***
## A     153.3669    24.2442   6.326 4.03e-10 ***
## k      44.7379     8.6216   5.189 2.64e-07 ***
## s       1.4762     0.2154   6.854 1.36e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4524 on 865 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 2.869e-06
##   (348 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq  Df Sum Sq F value    Pr(>F)    
## 1   1211     309.99                                 
## 2    864     175.99 347    134  1.8957 6.464e-14 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model       AIC
## 1    2b  8998.361
## 2     4 12724.990
## 3     5  8995.414
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     0.5935     0.4294   1.382  0.16727    
## alpha   0.7684     0.1126   6.824 1.67e-11 ***
## a      24.4359     7.1577   3.414  0.00067 ***
## b      91.9391    13.0777   7.030 4.19e-12 ***
## c     114.3717    17.3683   6.585 7.89e-11 ***
## d       1.2279     0.1998   6.146 1.21e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4513 on 864 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (348 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.97063, p-value = 3.094e-12
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -8.1225, p-value = 4.569e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

255 - Prairie Parkland (Subtropical)

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    408     218.09                                
## 2    384     184.75 24 33.343  2.8877 1.026e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 4302.110
## 2     2 4087.713
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -0.4395     0.4776  -0.920 0.358043    
## alpha   0.5924     0.1622   3.652 0.000297 ***
## A     191.8035    37.3817   5.131 4.59e-07 ***
## k      52.7150    12.4724   4.227 2.97e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6936 on 384 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 1.496e-06
##   (24 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)   
## 1    384     184.75                             
## 2    383     181.12  1 3.6224  7.6598 0.00592 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 4087.713
## 2    2a 4082.029
## 3    2b 4087.527
## 4    2c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau    -0.35911    0.49401  -0.727 0.467710    
## alpha   0.58110    0.14985   3.878 0.000124 ***
## A     289.31044  134.85478   2.145 0.032553 *  
## k     128.69919   90.87880   1.416 0.157541    
## p       0.04193    0.01342   3.124 0.001922 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6877 on 383 degrees of freedom
## 
## Number of iterations to convergence: 17 
## Achieved convergence tolerance: 6.545e-06
##   (24 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    406     207.53                                
## 2    382     171.16 24 36.375  3.3827 2.915e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2a 4082.029
## 2     4 4285.720
## 3     5 4062.072
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -0.3922     0.4717  -0.831    0.406    
## alpha   0.6720     0.1409   4.768 2.65e-06 ***
## a      24.3766     3.5771   6.815 3.69e-11 ***
## b      78.2871    10.8889   7.190 3.45e-12 ***
## c      56.0643     6.1528   9.112  < 2e-16 ***
## d       0.9506     0.1362   6.979 1.32e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6694 on 382 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (24 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.93842, p-value = 1.363e-11
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -4.4913, p-value = 7.078e-06
## alternative hypothesis: two.sided

predict and plot

plotting 2

261 - California Coastal Chaparral Forest and Shrub

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit

  • add s model: does not fit

  • add s+p model: does not fit

  • unable to fit model (only 64 observations)

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

262 - California Dry Steppe

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit

  • add s model: does not fit

  • add s+p model: does not fit

  • unable to fit model (0 observations)

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

263 - California Coastal Steppe - Mixed Forest and Redwood Forest

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

313 - Colorado Plateau Semi-Desert

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

315 - Southwest Plateau and Plains Dry Steppe and Shrub

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

321 - Chihuahuan Semi-Desert

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

322 - American Semidesert and Desert

model selection 1

## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
##   model AIC
## 1     1  NA
## 2     2  NA
## Warning in min(AIC1_322$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_322.' not found

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"
  • Cannot fit model
  • not enough data (only 3 observations)

331 - Great Plains/Palouse Dry Steppe

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"
  • Cannot fit model

332 - Great Plains Steppe

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1    141     88.067                         
## 2    127     75.692 14 12.375  1.4831 0.1264
##   model      AIC
## 1     1 1555.082
## 2     2 1422.430
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau      1.106      2.299   0.481    0.631    
## alpha    1.043      0.232   4.494 1.55e-05 ***
## A      167.129    102.643   1.628    0.106    
## k       86.630     58.626   1.478    0.142    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.772 on 127 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 4.906e-06
##   (15 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("f_", Mod.Sel1, "a", sep = "")), data = G_332,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("f_", Mod.Sel1, "b", sep = "")), data = G_332,  : 
##   number of iterations exceeded maximum of 50
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model     AIC
## 1     2 1422.43
## 2    2a      NA
## 3    2b      NA
## 4    2c      NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau      1.106      2.299   0.481    0.631    
## alpha    1.043      0.232   4.494 1.55e-05 ***
## A      167.129    102.643   1.628    0.106    
## k       86.630     58.626   1.478    0.142    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.772 on 127 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 4.906e-06
##   (15 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1    139     82.744                            
## 2    125     69.806 14 12.938  1.6548 0.07363 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 1422.430
## 2     4 1550.105
## 3     5 1415.826
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     1.5672     2.6040   0.602   0.5484    
## alpha   1.0506     0.2270   4.627 9.14e-06 ***
## a      26.2968    14.3835   1.828   0.0699 .  
## b      49.0289    25.3233   1.936   0.0551 .  
## c      90.3751    38.5828   2.342   0.0207 *  
## d       0.9109     0.4962   1.836   0.0688 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7473 on 125 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (15 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.87384, p-value = 3.588e-09
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -3.501, p-value = 0.0004635
## alternative hypothesis: two.sided

predict and plot

plotting 2

341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit

plot residuals

## [1] "cannot plot residuals"
  • model not fitted because only 62 observations

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

342 - Intermountain Semi-Desert

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

411 - Everglades

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

M211 - Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   3966     645.80                                
## 2   3952     609.53 14 36.262  16.793 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 42166.19
## 2     2 41840.90
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     1.07467    0.21865   4.915 9.24e-07 ***
## alpha   0.90960    0.06581  13.822  < 2e-16 ***
## A     386.41867   27.73826  13.931  < 2e-16 ***
## k     178.58145   13.13977  13.591  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3927 on 3952 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 1.553e-06
##   (14 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   3952     609.53                                
## 2   3951     605.64  1 3.8897  25.375 4.931e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 41840.90
## 2    2a 41817.58
## 3    2b 41800.23
## 4    2c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.92749    0.20677   4.486 7.47e-06 ***
## alpha   0.93841    0.06619  14.177  < 2e-16 ***
## A     217.97071   15.91105  13.699  < 2e-16 ***
## k      64.33797    6.20942  10.361  < 2e-16 ***
## s       1.38818    0.06640  20.907  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3907 on 3951 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 3.78e-06
##   (14 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   3964     637.04                                
## 2   3950     600.06 14 36.985   17.39 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2b 41800.23
## 2     4 42116.02
## 3     5 41782.90
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     1.00143    0.21329   4.695 2.75e-06 ***
## alpha   0.94619    0.06507  14.542  < 2e-16 ***
## a      21.16601    2.88388   7.339 2.59e-13 ***
## b     131.27072    8.83261  14.862  < 2e-16 ***
## c     156.42672   14.16203  11.046  < 2e-16 ***
## d       1.39288    0.09318  14.949  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3898 on 3950 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (14 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.98839, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -26.733, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

M221 - Eastern Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   4620     758.87                                
## 2   4593     719.43 27 39.437  9.3248 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 51198.35
## 2     2 50731.36
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.78480    0.14404   5.449 5.34e-08 ***
## alpha   0.91764    0.06205  14.789  < 2e-16 ***
## A     258.54261   10.28744  25.132  < 2e-16 ***
## k      59.04328    3.19504  18.480  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3958 on 4593 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 1.825e-06
##   (27 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value  Pr(>F)    
## 1   4593     719.43                               
## 2   4592     718.57  1  0.8579  5.4825 0.01925 *  
## 3   4592     714.19  0  0.0000                    
## 4   4591     703.14  1 11.0492 72.1436 < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 50731.36
## 2    2a 50727.88
## 3    2b 50699.74
## 4    2c 50630.06
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.95521    0.15274   6.254 4.37e-10 ***
## alpha   0.92578    0.06043  15.321  < 2e-16 ***
## A     159.86389    5.76420  27.734  < 2e-16 ***
## k      38.48498    1.13710  33.845  < 2e-16 ***
## p       0.24420    0.02081  11.736  < 2e-16 ***
## s       2.88617    0.24010  12.021  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3914 on 4591 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 3.107e-06
##   (27 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   4618     743.42                                
## 2   4591     702.06 27 41.361  10.018 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2c 50630.06
## 2     4 51107.25
## 3     5 50622.97
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.94893    0.15197   6.244 4.65e-10 ***
## alpha   0.92236    0.06059  15.223  < 2e-16 ***
## a      37.86675    3.02947  12.499  < 2e-16 ***
## b     115.58994    4.82746  23.944  < 2e-16 ***
## c     101.67398    3.95996  25.676  < 2e-16 ***
## d       1.19560    0.06247  19.140  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3911 on 4591 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (27 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.96838, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -26.709, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

M223 - Ozark Broadleaf Forest Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    523     64.694                                
## 2    521     60.692  2 4.0019  17.177 5.969e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 5359.324
## 2     2 5320.473
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau    -0.03335    0.28391  -0.117    0.907    
## alpha   0.95993    0.15629   6.142 1.62e-09 ***
## A     308.68739   47.34757   6.520 1.67e-10 ***
## k     100.73887   21.37371   4.713 3.13e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3413 on 521 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 9.364e-07
##   (3 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = G_M223,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    521     60.692                          
## 2    520     60.589  1 0.10356  0.8888 0.3462
##   model      AIC
## 1     2 5320.473
## 2    2a 5321.577
## 3    2b 5321.974
## 4    2c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau    -0.03335    0.28391  -0.117    0.907    
## alpha   0.95993    0.15629   6.142 1.62e-09 ***
## A     308.68739   47.34757   6.520 1.67e-10 ***
## k     100.73887   21.37371   4.713 3.13e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3413 on 521 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 9.364e-07
##   (3 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    521     64.501                                
## 2    519     60.606  2 3.8948  16.677 9.565e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 5320.473
## 2     4 5361.749
## 3     5 5323.726
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau    -0.03335    0.28391  -0.117    0.907    
## alpha   0.95993    0.15629   6.142 1.62e-09 ***
## A     308.68739   47.34757   6.520 1.67e-10 ***
## k     100.73887   21.37371   4.713 3.13e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3413 on 521 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 9.364e-07
##   (3 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.96244, p-value = 2.54e-10
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -8.9577, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

M231 - Ouachita Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    586     115.11                                
## 2    583     110.96  3 4.1518  7.2716 8.551e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 6079.429
## 2     2 6046.192
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     0.4484     0.4959   0.904 0.366192    
## alpha   0.8699     0.2292   3.795 0.000163 ***
## A     485.7390   149.6379   3.246 0.001237 ** 
## k     255.8678    86.8725   2.945 0.003355 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4363 on 583 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 2.808e-06
##   (3 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    583     110.96                          
## 2    582     110.64  1 0.31117  1.6368 0.2013
##   model      AIC
## 1     2 6046.192
## 2    2a 6046.543
## 3    2b 6914.673
## 4    2c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     0.4484     0.4959   0.904 0.366192    
## alpha   0.8699     0.2292   3.795 0.000163 ***
## A     485.7390   149.6379   3.246 0.001237 ** 
## k     255.8678    86.8725   2.945 0.003355 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4363 on 583 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 2.808e-06
##   (3 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    584     114.44                                
## 2    581     110.29  3 4.1455  7.2793 8.464e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 6046.192
## 2     4 6079.986
## 3     5 6046.664
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     0.4484     0.4959   0.904 0.366192    
## alpha   0.8699     0.2292   3.795 0.000163 ***
## A     485.7390   149.6379   3.246 0.001237 ** 
## k     255.8678    86.8725   2.945 0.003355 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4363 on 583 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 2.808e-06
##   (3 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.96265, p-value = 4.65e-11
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -9.4958, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

M242 - Cascade Mixed Forest

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

M261 - Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq  Df Sum Sq F value Pr(>F)
## 1    308     94.545                          
## 2    150     49.447 158 45.098  0.8659 0.8142
##   model      AIC
## 1     1 3309.570
## 2     2 1656.873
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)  
## tau    -1.4572     1.4782  -0.986   0.3258  
## alpha   0.7454     0.2859   2.607   0.0101 *
## A     189.4205   134.0559   1.413   0.1597  
## k      12.1167    10.5064   1.153   0.2506  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5741 on 150 degrees of freedom
## 
## Number of iterations to convergence: 10 
## Achieved convergence tolerance: 6.427e-06
##   (158 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    150     49.447                          
## 2    149     49.248  1 0.19855  0.6007 0.4395
##   model      AIC
## 1     2 1656.873
## 2    2a 1658.254
## 3    2b       NA
## 4    2c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)  
## tau    -1.4572     1.4782  -0.986   0.3258  
## alpha   0.7454     0.2859   2.607   0.0101 *
## A     189.4205   134.0559   1.413   0.1597  
## k      12.1167    10.5064   1.153   0.2506  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5741 on 150 degrees of freedom
## 
## Number of iterations to convergence: 10 
## Achieved convergence tolerance: 6.427e-06
##   (158 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq  Df Sum Sq F value Pr(>F)
## 1    306     91.857                          
## 2    148     47.700 158 44.157  0.8671 0.8111
##   model      AIC
## 1     2 1656.873
## 2     4 3304.600
## 3     5 1655.335
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -1.5315     1.3560  -1.129    0.261    
## alpha   0.6259     0.3236   1.934    0.055 .  
## a       0.0000   186.8284   0.000    1.000    
## b     186.0902   217.3750   0.856    0.393    
## c     116.1885    19.5549   5.942 1.94e-08 ***
## d       1.8167     1.2953   1.402    0.163    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5677 on 148 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (158 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.981, p-value = 0.03198
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = 1.0065, p-value = 0.3142
## alternative hypothesis: two.sided

predict and plot

plotting 2

M262 - California coastal range - coniferous forest - open woodland - shrub meadow

Model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit

plot residuals

## [1] "cannot plot residuals"
  • model can fit - but K is negative (only 19 observations) - model excluded

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M313 - Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M331 - Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M332 - Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M333 - Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M334 - Black Hills Coniferous Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1    247     102.69                         
## 2    176      77.97 71 24.724   0.786 0.8767
##   model      AIC
## 1     1 2514.590
## 2     2 1827.743
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -0.4470     0.9878  -0.453  0.65143    
## alpha   0.7713     0.2129   3.623  0.00038 ***
## A     113.8241    36.5520   3.114  0.00215 ** 
## k      50.8899    25.0112   2.035  0.04338 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6656 on 176 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 6.267e-06
##   (74 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("f_", Mod.Sel1, "a", sep = "")), data = G_M334,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = G_M334,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##   Res.Df Res.Sum Sq  Df  Sum Sq F value Pr(>F)
## 1    176     77.970                           
## 2    212     86.587 -36 -8.6171  0.5403 0.9845
## 3    175     77.471  37  9.1156  0.5565 0.9814
## 4    211     86.173 -36 -8.7017  0.5460 0.9830
##   model      AIC
## 1     2 1827.743
## 2    2a 2168.486
## 3    2b 1828.588
## 4    2c 2169.446
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -0.4470     0.9878  -0.453  0.65143    
## alpha   0.7713     0.2129   3.623  0.00038 ***
## A     113.8241    36.5520   3.114  0.00215 ** 
## k      50.8899    25.0112   2.035  0.04338 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6656 on 176 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 6.267e-06
##   (74 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1    245    102.324                         
## 2    174     77.733 71  24.59  0.7753 0.8895
##   model      AIC
## 1     2 1827.743
## 2     4 2517.688
## 3     5 1831.196
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -0.4470     0.9878  -0.453  0.65143    
## alpha   0.7713     0.2129   3.623  0.00038 ***
## A     113.8241    36.5520   3.114  0.00215 ** 
## k      50.8899    25.0112   2.035  0.04338 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6656 on 176 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 6.267e-06
##   (74 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.93019, p-value = 1.28e-07
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -3.836, p-value = 0.0001251
## alternative hypothesis: two.sided

predict and plot

plotting 2

M341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2


Fitted parameters

Best / selected models by ecoprovince

Code Ecoregion Sel.Mod.2 Sel.Mod.3 Best.Mod
211 Northeastern Mixed Forest 2b 5 5
212 Laurentian Mixed Forest 2c 5 5
221 Eastern Broadleaf Forest 2b 5 5
222 Midwest Broadleaf Forest 2a 5 5
223 Central Interior Broadleaf Forest 2b 5 5
231 Southeastern Mixed Forest 2c 5 5
232 Outer Coastal Plain Mixed Forest 2c 5 5
234 Lower Mississippi Riverine Forest 2 2 2
242 Pacific Lowland Mixed Forest NA NA NA
251 Prairie Parkland (Temperate) 2b 5 5
255 Prairie Parkland (Subtropical) 2a 5 5
261 California Coastal Chaparral Forest and Shrub NA NA NA
262 California Dry Steppe NA NA NA
263 California Coastal Steppe - Mixed Forest and Redwood Forest NA NA NA
313 Colorado Plateau Semi-Desert NA NA NA
315 Southwest Plateau and Plains Dry Steppe and Shrub NA NA NA
321 Chihuahuan Semi-Desert NA NA NA
322 American Semidesert and Desert NA NA NA
331 Great Plains/Palouse Dry Steppe NA NA NA
332 Great Plains Steppe 2 5 5
341 Intermountain Semi-Desert and Desert NA NA NA
342 Intermountain Semi-Desert NA NA NA
411 Everglades NA NA NA
M211 Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow 2b 5 5
M221 Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow 2c 5 5
M223 Ozark Broadleaf Forest Meadow 2 2 2
M231 Ouachita Mixed Forest 2 2 2
M242 Cascade Mixed Forest NA NA NA
M261 Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow 2 5 5
M262 California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow NA NA NA
M313 Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow NA NA NA
M331 Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow NA NA NA
M332 Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow NA NA NA
M333 Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow NA NA NA
M334 Black Hills Coniferous Forest 2 2 2
M341 Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow NA NA NA

table by ecoprovince

Code Ecoregion region n.obs n.plots tau tau.variance tau.2.5 tau.97.5 alpha alpha.variance alpha.2.5 alpha.97.5 A A.2.5 A.97.5 k k.2.5 k.97.5 a a.2.5 a.97.5 b b.se b.2.5 b.97.5 c c.2.5 c.97.5 d d.2.5 d.97.5
211 Northeastern Mixed Forest east 4838 2419 0.9424031 0.0521622 0.4946206 1.3901857 1.1732355 0.0047294 1.0384042 1.3080667 296.7106 215.43507 377.9862 99.70219 56.952511 142.45188 37.60901 33.322363 41.89566 107.76147 NA 95.706112 119.81683 115.49056 104.46666 126.51445 0.9314542 0.8278945 1.035014
212 Laurentian Mixed Forest east 12962 6481 0.4443891 0.0257410 0.1298840 0.7588942 0.9081521 0.0018684 0.8234201 0.9928841 118.3477 106.87534 129.8200 45.43189 41.657800 49.20598 22.73882 20.282002 25.19564 81.87877 NA 74.767183 88.99036 123.26490 109.93388 136.59592 1.3351866 1.2160475 1.454326
221 Eastern Broadleaf Forest east 5446 2723 0.6042576 0.0270982 0.2815289 0.9269862 0.9247619 0.0026709 0.8234423 1.0260816 269.9856 227.18055 312.7906 61.89490 48.633836 75.15597 27.90793 21.861033 33.95484 151.78065 NA 134.724680 168.83662 133.03972 112.19726 153.88218 1.3181638 1.1569938 1.479334
222 Midwest Broadleaf Forest east 3552 1776 0.2253071 0.0809640 -0.3327003 0.7833144 0.9764315 0.0056993 0.8283833 1.1244797 400.6133 278.35898 522.8677 146.96501 83.136845 210.79317 24.12342 19.205295 29.04154 119.93339 NA 101.854303 138.01247 106.27003 91.94773 120.59233 1.0400449 0.8989773 1.181113
223 Central Interior Broadleaf Forest east 6388 3194 -0.0886365 0.0142121 -0.3223588 0.1450858 0.8518610 0.0031213 0.7423297 0.9613923 191.8396 170.01911 213.6601 40.42488 34.501375 46.34838 29.94864 24.324500 35.57278 116.92622 NA 106.512186 127.34025 104.05803 92.83853 115.27754 1.2094657 1.0688136 1.350118
231 Southeastern Mixed Forest east 7790 3895 1.5683967 0.0312611 1.2217888 1.9150045 0.8342248 0.0021951 0.7423777 0.9260719 160.4121 143.82410 177.0001 34.73716 30.933723 38.54059 16.88730 13.689232 20.08536 127.95506 NA 113.143429 142.76670 137.97804 105.69057 170.26552 1.7878861 1.5850468 1.990725
232 Outer Coastal Plain Mixed Forest east 7940 3970 1.1715993 0.0405997 0.7766012 1.5665975 0.8093879 0.0019352 0.7231514 0.8956244 158.5355 140.11780 176.9532 36.29188 32.120973 40.46279 20.89438 17.407091 24.38167 127.00119 NA 110.019361 143.98302 137.92562 102.90745 172.94379 1.6773002 1.4613897 1.893211
234 Lower Mississippi Riverine Forest east 830 415 0.5365186 0.2303423 -0.4058930 1.4789303 0.8974205 0.0106700 0.6945892 1.1002519 578.9666 300.52578 857.4075 194.26139 87.747074 300.77571 NA NA NA NA NA NA NA NA NA NA NA NA NA
242 Pacific Lowland Mixed Forest pacific 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
251 Prairie Parkland (Temperate) east 1392 696 0.5935494 0.1844038 -0.2492842 1.4363829 0.7683810 0.0126797 0.5473712 0.9893908 153.3669 105.78254 200.9513 44.73786 27.816115 61.65961 24.43590 10.387458 38.48434 91.93913 NA 66.271403 117.60686 114.37173 80.28268 148.46079 1.2279283 0.8357726 1.620084
255 Prairie Parkland (Subtropical) east 444 222 -0.3921830 0.2224859 -1.3196054 0.5352393 0.6719845 0.0198603 0.3948956 0.9490735 289.3104 24.16204 554.4588 128.69919 -49.984634 307.38301 24.37657 17.343350 31.40978 78.28708 NA 56.877418 99.69675 56.06428 43.96678 68.16178 0.9505970 0.6827878 1.218406
261 California Coastal Chaparral Forest and Shrub pacific 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
262 California Dry Steppe pacific 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
263 California Coastal Steppe - Mixed Forest and Redwood Forest pacific 4 2 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
313 Colorado Plateau Semi-Desert interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
315 Southwest Plateau and Plains Dry Steppe and Shrub interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
321 Chihuahuan Semi-Desert interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
322 American Semidesert and Desert interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
331 Great Plains/Palouse Dry Steppe interior west 118 59 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
332 Great Plains Steppe interior west 154 77 1.5671503 6.7810091 -3.5865623 6.7208629 1.0505657 0.0515516 0.6012062 1.4999252 167.1286 -35.98320 370.2403 86.63024 -29.379580 202.64005 26.29682 -2.169919 54.76357 49.02886 NA -1.089147 99.14686 90.37508 14.01489 166.73527 0.9108652 -0.0711632 1.892894
341 Intermountain Semi-Desert and Desert interior west 4 2 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
342 Intermountain Semi-Desert interior west 2 1 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
411 Everglades east 66 33 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M211 Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow east 5108 2554 1.0014343 0.0454934 0.5832618 1.4196067 0.9461881 0.0042335 0.8186231 1.0737531 217.9707 186.77606 249.1654 64.33797 52.163996 76.51195 21.16601 15.511965 26.82005 131.27072 NA 113.953817 148.58763 156.42672 128.66114 184.19229 1.3928757 1.2101952 1.575556
M221 Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow east 5186 2593 0.9489282 0.0230962 0.6509857 1.2468707 0.9223633 0.0036710 0.8035806 1.0411460 159.8639 148.56328 171.1645 38.48498 36.255709 40.71424 37.86675 31.927529 43.80597 115.58994 NA 106.125791 125.05408 101.67398 93.91056 109.43740 1.1955984 1.0731328 1.318064
M223 Ozark Broadleaf Forest Meadow east 602 301 -0.0333485 0.0806076 -0.5911068 0.5244099 0.9599312 0.0244255 0.6529016 1.2669608 308.6874 215.67178 401.7030 100.73887 58.749635 142.72811 NA NA NA NA NA NA NA NA NA NA NA NA NA
M231 Ouachita Mixed Forest east 680 340 0.4484485 0.2459056 -0.5254974 1.4223945 0.8699411 0.0525445 0.4197321 1.3201501 485.7390 191.84391 779.6341 255.86783 85.246686 426.48898 NA NA NA NA NA NA NA NA NA NA NA NA NA
M242 Cascade Mixed Forest pacific 34 17 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M261 Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow pacific 330 165 -1.5315111 1.8388175 -4.2111926 1.1481704 0.6259333 0.1047002 -0.0134886 1.2653553 189.4205 -75.46132 454.3022 12.11667 -8.643067 32.87642 0.00000 -369.195820 369.19582 186.09019 NA -243.469483 615.64987 116.18850 77.54570 154.83130 1.8166738 -0.7430680 4.376416
M262 California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow interior west 8 4 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M313 Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M331 Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M332 Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow interior west 20 10 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M333 Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow interior west 22 11 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M334 Black Hills Coniferous Forest interior west 306 153 -0.4470264 0.9757402 -2.3964750 1.5024223 0.7712933 0.0453143 0.3511838 1.1914028 113.8241 41.68754 185.9606 50.88991 1.529410 100.25040 NA NA NA NA NA NA NA NA NA NA NA NA NA
M341 Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA

plot tau

map

## OGR data source with driver: ESRI Shapefile 
## Source: "C:\Users\hogan.jaaron\Dropbox\FIA_R\Mapping\S_USA.EcoMapProvinces\S_USA.EcoMapProvinces.shp", layer: "S_USA.EcoMapProvinces"
## with 37 features
## It has 17 fields
## Integer64 fields read as strings:  PROVINCE_ PROVINCE_I

plot alpha (biomass compensation effect)

plot A (asymptote of B)

## Warning: Removed 19 rows containing missing values (`geom_point()`).

plot k (stand age at half biomass asymptote)

## Warning: Removed 19 rows containing missing values (`geom_point()`).

Caclulations - weighted averages

ge (stand biomass enhancement factor in % 2000-2021)

##          region weighted.tau weighted.tau.std_Error 95 % CI, upper
## 1     entire US  0.722177703            0.061043361    0.841822689
## 2       pacific -0.007869066            0.006967426    0.005787089
## 3          east  0.728418907            0.060138268    0.846289912
## 4 interior west  0.001627862            0.007818922    0.016952949
##   95 % CI, lower
## 1     0.60253272
## 2    -0.02152522
## 3     0.61054790
## 4    -0.01369722

alpha (biomass compensation effect)

##          region weighted.alpha weighted.alpha.std_Error 95 % CI, upper
## 1     entire US    0.900290679             5.428050e-07    0.900291743
## 2       pacific    0.003216112             5.177211e-08    0.003216213
## 3          east    0.890880769             5.391401e-07    0.890881825
## 4 interior west    0.006193798             3.584505e-08    0.006193868
##   95 % CI, lower
## 1    0.900289615
## 2    0.003216010
## 3    0.890879712
## 4    0.006193728

A (asymptote of forest biomass in Mg/ha)

##          region weighted.A
## 1     entire US   202.4230
## 2       pacific   169.8607
## 3          east   203.6845
## 4 interior west     0.0000

K (stand age at half maturation in years)

##          region weighted.k
## 1     entire US   59.53607
## 2       pacific   10.86550
## 3          east   59.95906
## 4 interior west   45.60468

Model Bookeeping

1. Delta-B due to Delta-STDAGE

2. Delta-B due to Delta-Year (ge)

make a fig

## Warning: Removed 10136 rows containing missing values (`geom_point()`).

3. stand age densities

make a fig

## Picking joint bandwidth of 7.36